On a Family of Non-Volterra Quadratic Operators Acting on a Simplex

  1. Jamilov, Uygun 1
  2. Ladra, Manuel 2
  1. 1 Institute of Nuclear Physics
    info

    Institute of Nuclear Physics

    Taskent, Uzbekistán

    ROR https://ror.org/01136x372

  2. 2 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2020

Volumen: 19

Número: 3

Tipo: Artículo

DOI: 10.1007/S12346-020-00433-X DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Qualitative theory of dynamical systems

Resumen

In the present paper, we consider a convex combination of non-Volterra quadratic stochastic operators defined on a finite-dimensional simplex depending on a parameter α and study their trajectory behaviours. We showed that for any α∈[0,1) the trajectories of such operator converge to a fixed point. For α=1 any trajectory of the operator converges to a periodic trajectory.

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